Subgroups — C₇⋊#16812841 #37567955

Order 24444.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₃×C₉₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₉₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇×C₉₇	—	6	2	no	—
4	#16812841	—	7	1	no	maximal, Hall
5	Dic₆₇₉	—	9	1	no	maximal, Hall
6	C₃×C₇×C₉₇	—	2	2	no	—
7	C₃⋊D₃×C₉₇	D₇	1	1	yes	characteristic
8	C₂×C₇×C₉₇	—	9	1	no	—
9	C₃²×C₉₇	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₉₇	#157	1	1	yes	characteristic, complemented, Hall
11	D₃×C₉₇	—	6	2	no	—
12	Dic₉₇	—	63	1	no	Hall
13	C₃×C₉₇	—	2	2	no	—
14	C₇⋊#157	—	97	1	no	maximal, Hall
15	C₂×C₉₇	—	9	1	no	—
16	C₇×C₃⋊D₃	D₉₇	1	1	yes	characteristic
17	C₉₇	C₇⋊#157	1	1	yes	characteristic, complemented, Sylow
18	C₃²×C₇	Dic₉₇	1	1	yes	characteristic, complemented, Hall
19	D₃×C₇	—	6	2	no	—
20	#157	—	679	1	no	Hall
21	Dic₇	—	873	1	no	Hall
22	C₃×C₇	—	2	2	no	—
23	C₃⋊D₃	D₆₇₉	1	1	yes	characteristic
24	C₂×C₇	—	9	1	no	—
25	C₃²	Dic₆₇₉	1	1	yes	characteristic, complemented, Sylow
26	C₇	#16812841	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	6111	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇×C₉₇	C₄
prime radical, cosocle	C₇×C₃⋊D₃×C₉₇	C₂
LCS	G ▷ C₃²×C₇×C₉₇
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.